I think like every dumbass American thinks that if taxes and regulations on the rich are low enough, they'll be the next Bezos or Musk; they also think that an $8k voucher is going to enable them to send their kids to St. Marks, Hockaday, Kinkaid, Country Day, etc. Which is ironic, because the best of those schools are probably as classically liberal and elite as any you'll find.
Of course, the real schools they might be able to afford will be grifty-fraudy fundagelical schools whose "education" aligns with current "conservative" thinking and will leave them ill-equipped to do anything real in the world except run for office on a MAGA ticket.
And, it enables those who can't afford to move from "diverse" districts and schools to believe that they can finally get their kids away from the dirty darkies.
Also, I think there's some vague appeal, like "small government" and "local control" (illusory of course), to letting people out of the "socialism" of paying for education of other people's kids.